Most 7-foot Olympic barbells in gyms will weigh 45 lbs/20 kg.
You'd want to record the total weight used for the exercise, which would include the bar. The stress from the load won't deduct 45 lbs for bar weight, so you shouldn't either.
Adaptation can take some time, esp. if you're a beginner. It's not just muscles getting stronger, it's connective tissues, heart/lungs, nervous system, a lot of systems in your body go into weight training and exercise in general that we don't usually think about. All of these things are developing at different rates.
Be patient. Strength gains will come if you're smart about it, and the last thing you want is an injury because you added too much too quickly.
See the other thread about bar position for squats, chances are you've got it in the wrong place.
If the weights are challenging, then stick with them. You'll adapt with time and be able to add weight.
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